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United States Patent |
5,033,030
|
Goodman
|
July 16, 1991
|
Turbulence velocimetry technique
Abstract
A technique for obtaining a class of beam patterns is described which
results in eliminating the Doppler spread effect of the mean transverse
component of flow of scatterers. This is accomplished by weighting various
array elements. This component of flow is typically the main contributor
to Doppler frequency spread. With this component eliminated, the other
contributor of Doppler spread is due to the turbulent or fluctuating
scatterer motion on the scale of the scattering volume. This contributor
is smaller of the two and is estimated by standard Doppler methods.
Inventors:
|
Goodman; Louis (Middletown, RI)
|
Assignee:
|
The United States of America as represented by the Secretary of the Navy (Washington, DC)
|
Appl. No.:
|
533603 |
Filed:
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June 5, 1990 |
Current U.S. Class: |
367/89; 367/90 |
Intern'l Class: |
G01S 015/00 |
Field of Search: |
367/89,90
73/861.18,861.25
364/565
|
References Cited
Other References
Goodman, Doppler Statistics of Ocean Velocity Variability, Jun. 6, 1989,
43-53.
Hermitte et al., "Multibeam Doppler Sonar Observation of Tidal Flow
Turbulence", Geophys. Letters, 1983, pp. 717-720.
|
Primary Examiner: Pihulic; Daniel T.
Attorney, Agent or Firm: McGowan; Michael J., Lall; Prithvi C.
Goverment Interests
STATEMENT OF GOVERNMENT INTEREST
The invention described herein may be manufactured and used by or for the
Government of the United States of America for governmental purposes
without the payment of any royalties thereon or therefor.
Claims
What is claimed is:
1. A method for determining contribution due to turbulence in a Doppler
spread function caused by the motion of scatterers in a scattering volume
in a body of water using a multi-element planar acoustic array which
includes the steps of:
using an element of said multi-element planar acoustic array as a projector
to transmit a first acoustic signal and thereafter a second acoustic
signal into said scattering volume;
measuring back scattered parts of said first acoustic signal and said
second acoustic signal from said scattering volume using all elements of
said multi-element planar acoustic array as receivers;
computing a weighting factor corresponding to each of said back scattered
parts of said first acoustic signal and second acoustic signal as received
by each element of said multi-element planar acoustic array;
multiplying each of said back scattered parts of said first acoustic signal
and said second acoustic signal as received by each element of said
multi-element planar acoustic array by a corresponding weighing factor to
obtain a plurality of weighted back scattered signals due to said first
acoustic signal and due to said second acoustic signal;
computing a weighted average of said weighted back scattered acoustic
signals due to said first acoustic signal and said second acoustic signal;
multiplying the weighted back scattered acoustic signals for a first pulse
pair formed by said first and said second acoustic signals;
repeating the process for multiplying the weighted back scattered acoustic
signals corresponding to a plurality of pulse pairs similar to said first
pulse pair; and
finding the average of the products of the two weighted back scattered
acoustic signals for said plurality of pulse pairs which is a measure of
said Doppler spread function having contribution due to turbulence.
2. The method of claim 1 wherein the step of determining a weighting factor
for each of said scattered acoustic signal includes taking square root of
the sinc function.
3. The method of claim 1 which further includes the step of normalizing the
contribution due to the transverse component of velocity perpendicular to
the acoustic axis to unity.
4. The method of claim 1 which includes the step of using every member of
said multi-element planar acoustic array for transmitting and receiving
acoustic signals.
Description
BACKGROUND OF THE INVENTION
(1) Field of the Invention
This invention generally relates to the field of fluid flow measurements
and more specifically to a turbulence velocimetry technique by obtaining
the Doppler spread of an acoustic signal only due to turbulent or
fluctuating motion of scatterers in a fluid such as water.
(2) Statement of the Prior Art
It is becoming increasingly essential to know about fluid flow for ocean
waters as it affects movements of ships therethrough. Furthermore,
detection of the ships and the like, while at sea, is also important.
Additionally, limiting the spreading of an oil spill in a body of water
and the distribution of nutrients in the ocean affecting its ecological
balance are also important. All these problems involve the study of
turbulence fluid flow in the ocean. Thus it is desirable to estimate
turbulence in the ocean and its impact under different conditions.
Doppler acoustic techniques are becoming increasingly important in fluid
flow measurements. Estimation is typically made of the component of motion
of the acoustic scatterers' parallel to the acoustic axis by locating the
mean Doppler spectrum. This Doppler shift must be estimated within the
zone of the Doppler spread or variance of this shift. The mean component
of flow, which is defined as the spatial average over a scattering volume,
in the direction of the acoustic axis produces a Doppler shift in the
projected frequency from f.sub.O to f.sub.O +.DELTA.f.sub.O. There is also
an accompanying Doppler spread, (.DELTA.f) of the spectrum due to the mean
vector velocity component of the scatterer motion in the direction
perpendicular to the acoustic axis and due to the turbulent or fluctuating
component of flow of the scatterers within the scattering volume. Thus
information on the vector components of fluid flow averaged over the
scattering volume and information on the fluctuating component of flow
within the scattering volume are contained in the Doppler spread spectrum.
It is thus desired to infer this fluid flow information from estimations
made of the Doppler spectrum.
Doppler spread, .DELTA.f, is typically the result of two components of the
fluid flow of the scatterers: (1) the mean vector velocity component in
the direction perpendicular to the acoustic axis and (2) the turbulent or
fluctuating component of fluid flow of the motion of the scatterers within
the scattering volume. In general, it is impossible to distinguish between
the effects of (1) and (2) which contribute to the Doppler spread. Thus
both of these components contribute to the uncertainty of a mean Doppler
estimate. In addition, it is not possible in general to use the Doppler
spread effects to estimate either the transverse flow or the turbulent
flow without a bias effect of one on the other. It is thus desirable to
eliminate one of the two components (i.e., transverse component of the
scatterers' motion) in order to get a realistic measurement of the other
(i.e., the component due to turbulent motion of the scatterers).
SUMMARY OF THE INVENTION
This invention is a technique for the specification of a beam pattern and,
in turn, a weighting function for a planar acoustic array, which results
in eliminating Doppler spread effects from the mean vector velocity
component in the direction perpendicular to the acoustic axis, i.e., due
to the transverse components of the velocities of the scatterers,
typically the most significant to the Doppler spread. With this component
eliminated, the turbulent component of the Doppler spread can be estimated
by standard techniques as discussed in "Multibeam Doppler Sonar
Observations of Tidal Flow Turbulence", R. L. Hermitte & H. Poor, Geophys.
Letters, 10, 8, 717-720 (1983) and "Measurements of Acoustic Correlation
in the Ocean with High Frequency Echosounder," Nature, 36, No. 580, pp.
1-3 (1983). This is basically accomplished by using a multi-element array
of (M).times.(N) elements, each element of the array being able to act as
a projector and a receiver. Two successive pulses are transmitted from an
element (taken to be a square for simplicity i.e., .DELTA.x=.DELTA.y). The
back scattered signals corresponding to each of the two transmitted
signals are received by every element of the planar acoustic array and
weighting factors are generated for every (receiver) element of the planar
acoustic array. They are Fourier transforms of the square root of the sinc
function, i.e.,
##EQU1##
The weighted received signals are then added for each of the two
transmitted signals forming a pulse pair to obtain two weighted signals
for the pulse pair. They are multiplied together. This process is repeated
with many other pulse pairs and an average of the product of the weighted
signals for different pulse pairs is taken so as to obtain the total
correlation function. The argument part of the weighting function is
normalized so as to eliminate the contribution to the correlation function
due to the effect of the transverse component of the velocities of the
scatterers. The remaining contribution to the correlation function is then
due to the turbulence effect only.
An object of subject invention is to estimate turbulence in a body of water
using Doppler techniques.
Another object of subject invention is to eliminate from the Doppler spread
effect the contribution due to the transverse component of the scatterers'
motion in the body of water.
Still another object of subject invention is to use the weighting technique
of the acoustic signal received by different elements of the planar
acoustic array.
Other objects, advantages and novel features of the invention will become
apparent from the following detailed description thereof when considered
in conjunction with the accompanying drawings wherein:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 diagrammatically shows a planar acoustic array with a plurality of
elements and the direction of propagation (i.e., acoustic axis) of an
acoustic signal from one of the elements towards a scattering volume.
FIG. 2 is a graphical representation of the Doppler shift and Doppler
spread caused by the motion of the scatterers in the scattering volume.
FIG. 3 is a schematic representation of a multi-element ((M) .times.(N))
planar acoustic array wherein each of the element can act either as a
projector or a receiver.
FIG. 4 is a display of the Doppler spread function with a 32 .times.32
element grid with each element being a square (i.e., .DELTA.x=.DELTA.y).
FIG. 5 is a graphical representation of the real part of the complex
weighting function for each element of the array.
FIG. 6 is a graphical representation of the beam pattern (magnitude and
directionality) required to produce the Doppler spread function of FIG. 4
which is unity over a certain period.
FIG. 7 is a graphical representation of the argument of the complex
weighting function for each element of the array.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to the drawings wherein like reference characters designate
identical or corresponding parts throughout various figures, FIG. 1 shows
a planar acoustic array 10 including multi-elements, each of which is
preferably represented as a square (i.e., .DELTA.x=.DELTA.y) for
convenience without losing any generality. Each element of the planar
acoustic array can act both as a projector and a receiver. As shown in
FIG. 1, element 12 transmits omnidirectional acoustic signal giving rise
to a wide beam pattern. The transmitted signal is back scattered by a
plurality of scatterers in scattering volume 16 and the back-scattered
acoustic signal is received by each individual element of the acoustic
array 10. The angular distance parameters are also shown in FIG. 1 as
.theta..sub.x & .theta..sub.y. Z-axis represents the acoustic axis and any
motion of the scatterers along the Z-axis introduces Doppler shift in the
acoustic signal of frequency f.sub.O, wave length .lambda. and acoustic
wave number .kappa.=2.pi..kappa.. This phase shift is due to the phase
change of the acoustic signal of frequency f.sub.O and wave length
.lambda.. The transverse component of the velocity is in the X-Y plane
(i.e., perpendicular to the Z-axis). Doppler shift .DELTA.f.sub.o, is
caused by the motion of the scatterers in the Z-direction and results in a
phase change in an acoustic signal and in the correlation function of the
received signals while the Doppler spread, .DELTA.f, results in a change
in an amplitude of the correlation function of the received signals and is
due to the transverse component of the motion of the scatterers and due to
the turbulent motion of the scatters.
After eliminating the contribution to the Doppler spread function due to
the transverse component of the velocities of the scatterers, the
remaining contribution to the correlation function is due to turbulent
motion of the scatterers.
FIG. 2 is a graphical representation of the Doppler shift (.DELTA.f.sub.O)
and Doppler spread (.DELTA.f) of the acoustic signal of frequency f.sub.o
and wavelength .lambda. resulting from the correlated and decorrelated
motions of the scatterers in scattering volume 16. Doppler spread is
represented by curve 18 which is symmetrical about point f.sub.0
+.DELTA.f.sub.0 along the frequency axis. FIG. 3 is a graphical
representation of planar acoustic array 10 with running indicies k and l
varying from -M2 to +M2 & -N/2 to+(N/2)-1 and an array 10 having
(M).times.(N) elements as shown in FIG. 3.
FIG. 4 is a graphical representation 20 of the Doppler spread function K
which represents only the transverse component of flow of motion of the
scatterers in the scattering volume 16.
As shown in the prior art in general and particularly in my article:
"Doppler Statistics of Ocean Variability" by Louis Goodman presented at
the Second Navy Independent Research/Independent Exploratory Development
Symposium at Naval Surface Warfare Center, Silver Spring, MD on 6-7 June
1989 wherein, Doppler spread correlation function K is given by
##EQU2##
where .OMEGA. is the solid angle associated with the beam; and
.kappa.=.theta.{sin(.kappa..sub.x),sin(.theta..sub.y)};
.kappa..sub.h
is the transverse scatterer velocity vector and .tau. is the time between
two successive transmitted acoustic signals to form a pulse pair and is
determined by the size of the acoustic array, range, etc.
K is obtained by using a beam pattern B (magnitude and directionality)
which can be shown to be related to weighting functions or factors
associated with various elements of the planar acoustic array 10, the
geometry (dimensions, etc.) of the array 10, scatterers in the scattering
volume 16 and the back-scattered acoustic signals received by each element
of the planar acoustic array. It can be shown that using back scattered
acoustic signals received by various elements of the planar acoustic array
10, the beam pattern B (magnitude and directionality) is given by
B=.intg..intg.dxdyW(x,y)exp-(i.kappa.xSin.theta..sub.x
+i.kappa.y.theta..sub.y)
where W(x,y) is the weighting factor associated with each element of the
array.
It can be shown that if we choose W(x,y) from the look-up tables, obtained
by numerical methods, for an array configuration of discrete (M).times.(N)
elements, in such a way that B, the beam pattern (magnitude and
directionality) is given by
##EQU3##
and .kappa.=acoustic wave number =2.pi./.lambda.. L.sub.x and L.sub.y are
the lengths of the acoustic planar array along the X-axis and Y-axis
respectively and angles .theta..sub.x and .theta..sub.y are the angular
distances as shown in FIG. 1.
With this requirement imposed upon the weighting factors for various
elements, we eliminate the contribution by the transverse component of
motion of the scatterers, leaving only the contribution due to turbulence.
FIG. 5 is a graphical representation 22 of the real part of the weighting
factors. FIG. 6 is a representation 24 of the beam pattern (magnitude and
directionality) and FIG. 7 is a representation 26 of the argument (phase
part) of the Doppler spread function. Combining the real part of the
Doppler spread function and the argument thereof we get the beam pattern
amplitude as shown in FIG. 6, which gives the Doppler spread function of
FIG. 4, which leaves only the contribution due to the turbulent motion of
the scatterers.
Consequently, following the teachings of the subject invention, the
technique for measuring turbulence represented by the motion of the
scatterers in a body of water using a multi-element planar acoustic array,
with each element acting as a projector and/or receiver, is as follows:
1. One of the acoustic elements of the array acts as a transmitter sending
first an acoustic signal along the acoustic axis into a scattering volume
having a plurality of scatterers in motion. The back-scattered acoustic
signals from each of the scatterers is received by each element of the
array. This gives a back-scattered received acoustic signal by each member
of the multi-element planar acoustic array of known dimensions.
2. From the look-up tables, numerically pre-computed, we get the weighting
function or factor for each element of the acoustic array. Multiply the
back-scattered received acoustic signal by each element by its
corresponding weighting function and add them together to obtain a number
represented by A (i.e., A=c.sub.11 W.sub.11 +c.sub.12 W.sub.12 +. . . ).
3. Repeat the same process by using a second acoustic pulse so as to obtain
a number B (i.e., B=C'.sub.11 W*.sub.1 +C'.sub.12 W*.sub.12 +. . . ). It
should be noted that W*.sub.11, W*.sub.12. . . are the complex conjugate
functions of W.sub.11, W.sub.12, respectively. Multiply A and B and take
the magnitude of [A.times.B] to get a number C.sub.1 for a pulse pair
given by acoustic signals 1 and 2. The time interval between the two
acoustic signals forming a pulse pair is determined by the characteristics
of the planar acoustic array and the range.
4. Repeat steps 1 through 3 for a number of pulse pairs to obtain C.sub.2,
C.sub.3, . . . . C.sub.R and find the average of these numbers
##EQU4##
Then C is a measure of turbulence as the remaining Doppler spread is due
to the turbulent motion of the scatterers in the scattering volume. This
information can be used to address the particular issue which is dependent
on the information regarding the turbulence in the fluid.
Briefly stated, estimation of turbulence in a body of water using the
technique of subject invention is obtained by using a planar multi-element
(M).times.(N) acoustic where each element can act either as a transmitter
or a receiver. A pulse pair comprising two acoustic signals which are
preselected time separation are transmitted by one of the elements of the
planar acoustic array. The pulse pair is back scattered by a plurality of
scatterers in motion due to turbulence inside a scattering volume and are
received by all elements of the planar acoustic array. The received
acoustic signals are weighted using the teachings of subject invention to
eliminate the effects of factors other than turbulence and thus get an
estimate of turbulence.
It will be understood that various changes in details, materials, steps and
arrangement of parts, which have been described in the preferred
embodiment to explain the teachings of subject invention. As an example,
the number of elements of the planar acoustic array can be varied.
Additionally, the size and configuration of the elements can also be
changed. The materials of which the elements of the array are made of can
also be changed without deviating from the teachings of subject invention.
It is therefore understood that within the scope of the appended claims
the invention may be practiced otherwise than as specifically described.
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